Fast convergence to nearly optimal solutions in potential games

Baruch Awerbuch, Yossi Azar, Amir Epstein, Vahab Seyed Mirrokni, Alexander Skopalik

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the speed of convergence of decentralized dynamics to approximately optimal solutions in potential games. We consider α-Nash dynamics in which a player makes a move if the improvement in his payoff is more than an α factor of his own payoff. Despite the known polynomial convergence of α-Nash dynamics to approximate Nash equilibria in symmetric congestion games [7], it has been shown that the convergence time to approximate Nash equilibria in asymmetric congestion games is exponential [25]. In contrast to this negative result, and as the main result of this paper, we show that for asymmetric congestion games with linear and polynomial delay functions, the convergence time of α-Nash dynamics to an approximate optimal solution is polynomial in the number of players, with approximation ratio that is arbitrarily close to the price of anarchy of the game. In particular, we show this polynomial convergence under the minimal liveness assumption that each player gets at least one chance to move in every T steps. We also prove that the same polynomial convergence result does not hold for (exact) best-response dynamics, showing the α-Nash dynamics is required. We extend these results for congestion games to other potential games including weighted congestion games with linear delay functions, cut games (also called party affiliation games) and market sharing games.

Original languageEnglish
Title of host publicationEC'08 - Proceedings of the 2008 ACM Conference on Electronic Commerce
Pages264-273
Number of pages10
DOIs
StatePublished - 2008
Event2008 ACM Conference on Electronic Commerce, EC'08 - Chicago, IL, United States
Duration: 8 Jul 200812 Jul 2008

Publication series

NameProceedings of the ACM Conference on Electronic Commerce

Conference

Conference2008 ACM Conference on Electronic Commerce, EC'08
Country/TerritoryUnited States
CityChicago, IL
Period8/07/0812/07/08

Keywords

  • Congestion games
  • Convergence time
  • Game theory
  • Nash equilibrium
  • Potential games
  • Price of anarchy

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